Answer:
[tex]2 \frac{10}{27}[/tex]
Step-by-step explanation:
4/3 to the power of 3 = to 4/3 x 4/3 x 4/3
which in the end equals to 64/27
there's no common factor between them to simplify, but we can turn them into a mixed number, which is 2 10/27 by dividing 64 and 27
The art teacher has 1 gallon of paint, which is enough for \frac{2}{3} of the class to complete a project.
How many gallons does she need for the whole class?
The teacher requires 1.5 gallons of paint for the whole class
Quantity of paint available with the teacher = 1 gallon
Fractions: In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Portion of the class covered by 1 gallon of paint = 2/3 class
Let x represent the whole class
Formulating the equation:
The portion of the class covered out of the whole class*Total class = Paint required for the portion of the class
So, for 2/3x = 1
x = 3/2
x = 1.5 gallon
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if test scores for an exam were normally distributed with a mean of 75 and a standard deviation of 5, find the probability that a randomly selected student scored less than 82
The probability that a randomly selected student in the class test scored marks which is less than 82 is 0.9192
It is given that in a test, the scores for an exam normally distributed has a mean of 75 and a standard deviation of 5. We have been asked to find the probability that a randomly selected student scored less than 82.
From the question we have,
Mean = 75
Standard deviation (SD) = 5
Therefore, the probability that a randomly chosen student has a score of less than 82 is represented as:
(P) Probability ( X < 82) = P { Z < [tex]\frac{82-75}{5}[/tex] }
= P {Z < 7/5}
= P {Z <1.4}
= Area from - ∞ to 1.4
= 0.9192
From the z table the area under the normal curve that corresponds to 1.4 is 0.9192
Hence the required probability of that a randomly selected student scored less than 82 is 0.9192
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A woman has a total of $15, 000 to invest. She invests part of the money in an account that pays 6% per year
and the rest in an account that pays 10% per year. If the interest earned in the first year is $1020, how much did
she invest in each account?
Answer:
$4,000 in the 10% per year account
$11,000 in the 12% per year account
What is the answerrrrrrr
Answer:
c
Step-by-step explanation:
c
Which of the given number sequences represents an arithmetic sequence?
A) 32, 16, 8, 4, 2,...
B 5, 10, 20, 40, 80,...
C)-4, -1/2, 3, 13/2, 10,…
D) 4, 8/3, 16/9, 32/27, 64/81,…
-4, -1/2, 3, 13/2, 10,… represents an arithmetic sequence.
An arithmetic sequence progresses with a common difference which is the difference of consecutive terms.
So for each of the number sequences, we will try to check if the consecutive terms has a common difference.
A) 32, 16, 8, 4, 2,...
16-32 = -16
8-16 = -8
4-8 = -4
2-4 = -2
As the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
B)5, 10, 20, 40, 80,...
10-5 = 5
20-10 = 10
40-20 = 20
80-40 = 40
Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
C) -4, -1/2, 3, 13/2, 10,…
-1/2- -4 = 7/2
3- -1/2 = 7/2
13/2-3 = 7/2
10-13/2 = 7/2
This sequence has a common difference and hence is an arithmetic sequence.
D) 4, 8/3, 16/9, 32/27, 64/81,…
8/3-4 = -4/3
16/9-8/3 = -8/9
32/27-16/9 = -16/27
64/81-32/27 = -32/81
Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
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8 circles and 20 squares what is the simplest ratio of total shapes
Answer
8:28 Hope this helps.
If m/3 = 4x + 10 and m/4 = 5x
find m/4.
Answer:
m/4 = 3x - 30
Step-by-step explanation:
Hello!
Let's subtract the second equation from the first equation:
[tex]\frac m3 = 4x + 10\\\frac m4 = 5x[/tex][tex]\frac m3 - \frac m4 = 4x + 10 - 5x[/tex]Now, solve for m.
Solve for m[tex]\frac m3 - \frac m4 = 4x + 10 - 5x[/tex]Multiply both sides by 12 to get rid of the denominators
[tex]4m - 3m = 48x + 120 - 60x[/tex][tex]-m = 120 - 12x[/tex][tex]m = 12x - 120[/tex]Plug in 12x - 120 for m in m/4
Find m/4[tex]\frac m4; m = 12x - 120[/tex][tex]\frac{12x - 120}{4}[/tex][tex]\frac{4(3x - 30)}{4}[/tex][tex]3x - 30[/tex]The value of m/4 is 3x - 30.
Hi , good afternoon/morning/night it would be really kind if u help.
Answer:
you can ask questions for clarification
Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $225. Now the cost is $310. What is the percent increase? Responses 38% 38% 27% 27% 73% 73%
The percentage increase in the cost of the airline tickets is 38%.
What is the percentage increase?Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency. In order to convert a value to a percentage, multiply the value by 100.
in order to determine the percentage increase, multiply the fraction of the change in price and the initial price by 100.
Percentage increase = (change in price / initial price) 100
Change in price = new price - initial price = $310 - $225 = $85
Initial price = $225
($85 / $225) x 100 = 38%
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A bar of steel is 300 cm long. amin cuts two 45 cm lengths off the bar. he then cuts the rest of the bar into as many 50 cm lengths as possible. work out how many 50 cm lengths of bar amin cuts.
Answer:
Here is your Answer and I'm from South Africa
Find the length of x and y
Answer:
y = 15/4 mm
x = 36/5 mm
Step-by-step explanation:
In similarity triangles, the corresponding sides are in same ratio.
[tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]
[tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]
2u - 17 = 11 solve for u simplify your answer as much as possible
Answer:
u = 14
Step-by-step explanation:
2u - 17 = 11
add 17 to both sides:
2u - 17 + 17 = 11 + 17
2u = 28
divide both sides by 2:
2u/2 = 28/2
u = 14
Determine the sum of the integers.
a. 4 + -11=
b. 21 +-3=
C. -9 + -4 =
d. 10-15 =
e. 7 + (-7)=
f. 12+ (-19) =
g. -13+ 13 =
h.
14+ (-20) =
Answer:
a -7
b 18
c -13
d -5
e 0
f -7
g 0
h -6
Step-by-step explanation:
too lazyy
Find b for the given line.
y = 3x + b; (2, 7)
The value of b for the given line is 1
What is equation of line ?The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.
Given that : y = 3x + b; (2, 7)
y =3x + b
7 = 6 + b
1 = b
The value of b for the given line is 1
The line's equation is a linear equation of degree one.
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What is 6 2/3 divided 1/5
Hello!
Let's solve:
[tex]\text{Write down the equation}\\\dfrac{6\dfrac{2}{3} }{\dfrac{1}{5} } \\\\\\\text{Convert the nominator, a mixed partial fraction to an improper fraction}\\\dfrac{\dfrac{20}{3} }{\dfrac{1}{5} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply its reciprocal}\\\dfrac{20}{3} *\dfrac{5}{1} = \dfrac{100}{3} \\\\\\\text{Convert the improper fraction back mixed partial fraction}\\\dfrac{100}{3} =33\dfrac{1}{3}[/tex]
Answer: [tex]\dfrac{100}{3} \text{ or }33\dfrac{1}{3}[/tex]
Hope that helps!
A delivery truck drives three routes in one day. The first route is 123 miles long, the second
route is 10 miles long, and the third route is 15 miles long.
What is the total number of miles the delivery truck drives?
To calculate the total number of miles the delivery truck drove, we add the lengths of the three routes together.
-> It drove 123 + 10 + 15 = 148 (miles).
− is 55 units to the right of 0
use the drop down menus to complete the statement about x
x is ------- units to the -------- 0
The value illustrated shows that x is -55 units to the left of 0.
How to illustrate the information?From the given statement we have the value of x is negative. Therefore, we need the complete statement about x being positive.
Therefore we have to put an alternate sign to the given statement we get -x is 55 units to the right of 0.
Negation to the given statement about x is -(-x) is -(55) units to the left of 0. The statement will be that x is -55 units to the left of 0.
By using the drop-down menus to complete the given statement about x is -55 units to the left of 0.
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if the divided is 782 and the divisor is 1523 what is the quotient
If the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.
What is dividend, divisor and quotient?
The dividend in this case refers to the number that is being divided. The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.
Let x be the quotient after dividing 782 by 1523.
[tex]\frac{782}{1523} = x\\0.5134 = x\\x = 0.51[/tex]
Therefore, if the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.
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Please help me. I fell asleep during class on accident and I missed steps on how to do this.
Reason:
The equation is in y = mx+b form where
m = 20 = slope
b = 0 = y intercept
The slope is the rate of change. It tells us how fast y increases.
slope = rise/run = 20 = 20/1
rise = 20 = increase the earnings by 20 dollars
run = 1 = each time the number of hours go up by 1
Find the sum of two hundred even numbers from 0 to 398
The sum of two hundred even numbers in the sequence from 0 to 398 is 39800
Sum of an APTo find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.
[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]
n = number of termsa = first termd = common differenceThe number of terms given here is 200, the first term is 0 and the common difference is 2
Substituting the values into the equation
[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]
The sum of two hundred even numbers from 0 to 398 is 39800
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The product of -3 and x is 18
Answer:
-6
Step-by-step explanation:
-3x = 18
divide both sides by -3
18 ÷ -3 = -6
Write an equation of a line that is parallel to 6x-2y=4 and goes through (-5,2)
Answer:
y = -1/3 x + 1/3
Step-by-step explanation:
In the picture.
Which answer choice is not a correct method to illustratethe answer to this problem?876 ÷ 43 = ?A) 876 ÷ 43 ≈ 20 B) 876 ÷ 43 = 20 16/43C) 876 ÷ 43 = 20.16D) 876 ÷ 43 = 20r16 note: the r stands for reminder
The answer to this question represents the possible choices that we have when solving a division.
When solving this division operation, and we use technology, we get the following result:
[tex]\frac{876}{43}=20.3720930233[/tex]Then, we can conclude that:
First CaseWe can conclude that the answer to this division is, approximately, 20. This could be an answer to this operation.
Second CaseIn this case, we can see the integer part of the answer, 20, and a fraction:
[tex]20\frac{16}{43}=20+\frac{16}{43}[/tex]And we know that:
[tex]undefined[/tex]g(a)=a²+2a-63 find g(8)
Answer:
g(8)=17
Step-by-step explanation:
Given :
g(a)=a²+2a-63
Substitute a = 8 :
g(8)=8^2+2(8)-63
= 64+16-63
=17
I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
The least common multiple for 12 and 15 is 60, the least common multiple for 6 and 15 is 30, and the least common multiple for 9 and 15 is 45.
What is the least common multiple?In mathematics, the term "least common multiple" is used to refer to a multiple of two or more numbers share and that is the smallest number possible.
How to identify the least common multiple?Mulitiply the numbers given by 1, 2, 3, 4, etc. until your find the first common number.
Lets use the numbers given
12 x 1 = 12 15 x 1 = 15
12 x 2 = 24 15 x 2 = 30
12 x 3 = 36 15 x 3 = 45
12 x 4 = 48 15 x 4 = 60
12 x 5 = 60
Based on this, the least common multiple is 60
6 x 1 = 6 15 x 1 = 15
6 x 2 = 12 15 x 2 = 30
6 x 3= 18
6 x 4 =24
6 x 5 =30
Based on this, the least common multiple is 30
9 x 1 = 9 15 x 1 = 15
9 x 2 = 18 15 x 2 = 30
9 x 3= 27 15 x 3 = 45
9 x 4 =36
9 x 5 =45
Based on this, the least common multiple is 45
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A Student recorded a temperature of 75 degrees Fahrhet at
hour 9 and 95 degrees fahreneit at hour 13.
- which caculation could be used to determine the avenge
rate of change between this two temperatures?
At hour 9, the temperature recorded was = 75 degrees
At hour 13, the temperature recorded was = 95 degrees
The rate of change = Change in the temperature / Change in the time
⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour
⇒ The rate of change = 20 degrees / 4 hours
⇒ The rate of change = 5 degrees per hour
What is meant by the Rate of change?The rate of change (ROC) measures how quickly a variable varies over a predetermined amount of time. When discussing momentum, the term ROC is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another.The momentum of a variable is represented by the rate of change, which is a mathematical term that describes the percent change in value over a specified period of time. Because it enables investors to identify trending securities and other trends, rate of change is a crucial financial term.Acceleration and deceleration are examples of rates of change with regard to speed or velocity. The slope of the line of best fit is used in statistics and regression modeling to determine the rate of change. It is the growth rate of the population. Momentum is a term frequently used in financial markets to describe rate of change.To learn more about the Rate of change, refer to:
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Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answer:13x9x6=702
Step-by-step explanation:
suppose that y is independent of explanatory variables and it takes on the values -2, -1, 0, 1, 1 with equal probability. does this violate the gauss- markov assumption
the parameters we are estimating using the OLS method must be themselves linear
What are the Gauss Markov assumptions?
Gauss Markov Assumptions
Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.
What are the properties of Gauss Markov Theorem?
The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.
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Diane wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 35 ft from the tree, and
Diane is standing 7.9 ft from the mirror, as shown in the figure. Her eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
The tree is approximately 27 ft tall if the answer is rounded off to the nearest foot when the similar triangle formula is applied.
What are properties of similar triangles?Two triangles can be said to be similar if their corresponding angles are seen as congruent and thereafter their corresponding sides are in proportion.
What are the 3 similar triangles?Similar Triangles Definition
Angle - Angle (AA)
Side - Angle - Side (SAS)
Side - Side - Side (SSS)Similar triangles are triangles that have the same shape, but their sizes may vary.
If Diane, mirror, and the exact bottom of the tree are placed as points on the ground all lying on one line, then the two right triangles can be stated as:
LEFT: y and 35 as the legs and unknown hypotenuse.
RIGHT: 6 and 7.9 as the legs and unknown hypotenuse.
The two angles pointed at the mirror are seen as of same measure that means that 35 and the hypotenuse of LEFT triangle makes same angle measure as the 7.9 and the hypotenuse of that of the RIGHT triangle.
Since these two are seen as similar triangles,
y/35 = 6/7.9
⇒y = 26.58
⇒ y ≈ 27 ft
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Deion's cab company charges a one-time pickup fee of $2 for every ride, as well as a $1.10 charge for each mile traveled. Find the rate of change.
Answer:
p=2+1.1m
Step-by-step explanation:
p=price, m=miles